Paul Pogba put in a fantastic man of the match display to help Manchester United towards a comfortable 2-0 win
The energetic Yannick Bolasie was Everton's main threat, scampering up and down the left hand side and swinging a couple of dangerous balls into the box.
Pogba was an influential figure, driving United forward in counter attacks and flashing a shot just wide from range in the 36th minute, although the Everton faithful thoroughly enjoyed seeing him tripping over the ball while attempting a piece of skill.
Wayne Rooney, facing the club where he spent 13 years of his career, didn't have a huge impact on the game, his main contribution being to receive a yellow card after a cynical foul from behind on Anthony Martial.
But United picked up a gear in the second half, and started very much on the front foot. Juan Mata stung the fingertips of Toffees keeper Jordan Pickford with a shot from the edge of the box just after the re-start, and then hit the post a few minutes later with a wonderful long range strike with the keeper beaten.
The Red Devils were now fully in control, and after lovely link-up play with Jesse Lingard Pogba shot wide again from a tight angle in the 54th minute.
But just two minutes later United finally took the lead, Pogba picking out Martial in the D, and the Frenchman delightfully curled a shot into the top corner. It was no less than they deserved.
Allardyce needed to take action, and withdrew Bolasie for Aaron Lennon and Rooney for James McCarthy, Rooney receiving a standing ovation from both sets of fans.
United continued to dominate but Oumar Niasse was guilty of wasting a big chance for Everton in the 70th minute, heading wide from a few yards out when he should have done better.
Everton continued to press but United still looked dangerous, Pickford saving brilliantly from a low Lingard drive.
But the match was effectively ended as a contest in the 81st minute, Pogba again in the thick of the action, setting up Lingard, who drove forward with the ball before curling a stunning strike into the net.